Question: Which decimal is equivalent to $\dfrac{76}{9}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $8.3$ (Choice B) B $8.\overline{3}$ (Choice C) C $8.\overline{4}$ (Choice D) D $8.4445$
Solution: $ \dfrac{76}{9}$ represents $76 \div 9 $. ${9}$ ${7}$ ${6}$ ${0}$ $\text{How many times does }9\text{ go into }{76}\text{?}$ ${8}$ ${7}$ ${2}$ $-$ ${4}$ ${76}\div9={8}\text{ with a remainder of }{4}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div9={4}\text{ with a remainder of }{4}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div9={4}\text{ with a remainder of }{4}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div9={4}\text{ with a remainder of }{4}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${4}$ ${3}$ ${6}$ $-$ ${4}$ ${4}$ ${40}\div9={4}\text{ with a remainder of }{4}$ Notice how the decimal is repeating and will continue to repeat as we bring down more zeros. So $\dfrac{76}{9}$ is equivalent to $8.\overline{4}$.